comes from phrase used for a secondary rail route, which branches of the main route. most branch lines are now closed in the UK. to say some one has there own branchline means they're a loner, weird and a bit lost in the head, also can be used in almost any situation possible cause its just funny.

1)John-
''What do you think of Nicole''
Me- ''Awh shes not all ther in the head , she has her own branch line that one'

2)David- Have you seen the television remote?
Me- Havent seen it in weeks id say it has own branch line at this stage!